A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

TL;DR

This paper investigates the fluctuations in the overlap probability distribution in mean-field spin glasses under a magnetic field, highlighting the impact of rare samples on the distribution's tail.

Contribution

It provides a numerical analysis of sample-to-sample fluctuations and the role of rare samples in the overlap distribution near the De Almeida-Thouless line.

Findings

Large tail in the overlap distribution caused by rare samples

Different techniques reveal the significance of rare sample contributions

Fluctuations are prominent in the presence of a magnetic field on the AT line

Abstract

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress on different aspects of the contribution of rare samples.